Parallel Transport along Seifert Manifolds and Fractional Monodromy

N. Martynchuk and K. Efstathiou
Communications in Mathematical Physics, 356(2), 427-449, 2017
DOI: 10.1007/s00220-017-2988-5
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Abstract

The notion of fractional monodromy was introduced by Nekhoroshev, Sadovskií and Zhilinskií as a generalization of standard (‘integer’) monodromy in the sense of Duistermaat from torus bundles to singular torus fibrations. In the present paper we prove a general result that allows one to compute fractional monodromy in various integrable Hamiltonian systems. In particular, we show that the non-triviality of fractional monodromy in 2 degrees of freedom systems with a Hamiltonian circle action is related only to the fixed points of the circle action. Our approach is based on the study of a specific notion of parallel transport along Seifert manifolds.